suppose a simple random sample of size n is taken from a population with unknown

Question

suppose a simple random sample of size n is taken from a population with unknown mean u and unknown standard deviation q. A (1-a). 100% confidence interval for u is given by lower bound: x-t a/2 * s/ n upper bound: x+Ta/2 . s/ n (1) Where T a/2 is computed with n-a degrees of freedom. Note the interval is exact when the population is normally distributed. It is approximately correct for nonnormal populations, provided that n is large enough.

a) Find the t-value such that the area in the right tail is 0.02 with degrees of freedom.

b) Find the t-value such that the area in the right tail is 0.10 with 32 degrees of freedom.

c) Find the t-value such that the area left of the t-value is 0.05 with 6 degrees of freedom (hint: Use symmetry)

Explanation / Answer

a)please revert on degree of freedom as it is not specified.

b) for 0.10 area on right tail and 32 degrees of freedom ; critical value of t =1.3086

c) for 0.05 area on left and 6 degree of freedom ; critical value of t = -1.9432

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